Geometrically nonlinear analysis of thin-shell structures based on an isogeometric-meshfree coupling approach

This paper develops a novel coupling approach of the isogeometric analysis (IGA) method and the meshfree method for geometrically nonlinear analysis of thin-shell structures. The Kirchhoff-Love (KL) thin-shell theory is employed without the consideration of rotational degrees of freedom. Both parametric domain and physical domain are utilized for the thin-shell structures, and the former one is used to couple the IGA and meshfree methods and to obtain the later one via mapping. The domain is divided into three subdomains: the subdomain described by the IGA method to ensure geometry exactness, the subdomain described by the meshfree method to achieve local refinement, and the coupling subdomain described by both methods. In the coupling subdomain, the reproducing points are obtained based on the consistency conditions to realize smoothness between the IGA and meshfree subdomains. The coupling approach can achieve a higher convergence rate than the IGA and meshfree methods because of the realization of local refinement. The accuracy and robustness of the coupling approach are validated by solving shell benchmark problems.